Patched conic approximation
In
astrodynamics, the patched conic approximation or patched two-body approximation[1][2] is a method to simplify trajectory calculations for spacecraft
in a multiple-body environment.
Method
The simplification is achieved by dividing space into various parts by assigning each of the n bodies (e.g. the
conic sections of the Kepler orbits
.
Although this method gives a good approximation of trajectories for
Lagrangian points
.
Example
On an
gravity well, then an elliptic or hyperbolic
trajectory in the Sun's sphere of influence is required to transfer from Earth's sphere of influence to that of Mars, etc. By patching these conic sections together—matching the position and velocity vectors between segments—the appropriate mission trajectory can be found.
See also
- Two-body problem
- N-body problem
- Sphere of influence
- Kerbal Space Program, a popular simulator based on the patched conic approximation
References
- LCCN 73157430.
- ^ Lagerstrom, P. A. and Kevorkian, J. [1963], Earth-to-moon trajectories in the restricted three-body problem, Journal de mecanique, p. 189-218.
- ISBN 978-0-615-24095-4.
Bibliography
- Carlson, K. M. (1970-11-30). An Analytical Solution to Patched-Conic Trajectories Satisfying Initial and Final Boundary Conditions (pdf). Technical Memorandum (Technical report). Bellcomm Inc. TM-70-2011-1.